Calculation of the Formation Energy of a Schottky Defect in Germanium

Hwang, Chi–Chuan; Watt, L.A.K.

doi:10.1103/physrev.171.958

Cited by 17 publications

(5 citation statements)

References 20 publications

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“…On the other hand, calculations with Table 2 Calculated formation (E F ) and migration (E M ) energies in eV of the uncharged intrinsic point defects in germanium [20] Band theory in one electron approximation 2.21 [21] Atomic orbital method 2.63 0.4 3.52(H) 0.09(H) [22,23] Perturbation theory of covalent crystals 3. 6 2.5(T) [24] Non-orthogonal tight-Binding method 1.93 2.3(D) [25][26][27][28] DFT with LDA approximation 3.55(D) [29] DFT with LDA approximation 2.6 0.4 [30] DFT with LDA approximation 2. the parameters proposed by Yu et al [14] and Nordlund et al [13] most probably yield underestimated values for the formation energy owing to large changes in the parameters e and s. Yu et al [14], in their parameters sets marked as B and S indeed reduced the energy scale parameter e by 10-14%, while Nordlund et al [13] reduced this parameter by 20%.…”

Section: The Formation and Migration Energy Of The Vacancymentioning

confidence: 99%

“…For that reason his results cannot be considered to be conclusive. Hwang and Watt [21] calculated the formation energy of the vacancy in Ge from first principles using the atomic orbital method. A fitting procedure was used in their calculations to reproduce the observed cohesive energy at the correlated lattice constant.…”

Section: Previous Calculationsmentioning

confidence: 99%

“…Pinto [30] suggests that, similar to the silicon vacancy [44], the high-temperature vacancy in Ge differs in properties from the low-temperature one. Taking into account that the MD simulations estimate neutral vacancy properties, and that the quenching experiments measure the concentration of a single-charged negative vacancy [21,45,46], and implementing the method proposed by Kro¨ger [46], one can estimate the formation energy of the neutral vacancy as suggested by Shaw [45], as follows.…”

Section: Experimental Values Of the Migration And Formation Energy Ofmentioning

confidence: 99%

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Molecular dynamics simulation of intrinsic point defects in germanium

Śpiewak

Muzyk

Kurzydłowski

et al. 2007

Journal of Crystal Growth

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Section: The Formation and Migration Energy Of The Vacancymentioning

confidence: 99%

Section: Previous Calculationsmentioning

confidence: 99%

Section: Experimental Values Of the Migration And Formation Energy Ofmentioning

confidence: 99%

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Molecular dynamics simulation of intrinsic point defects in germanium

Śpiewak

Muzyk

Kurzydłowski

et al. 2007

Journal of Crystal Growth

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“…The second term in E, can be calculated directly in the defect molecule approach (Larkins 1969) and is also given in table 4. Analogous calculations have been made for the vacancy in germanium by Hwang and Watt (1968). Third.…”

Section: Formation Energy Of the Single Vacancy (I) Molecular Orbitalmentioning

confidence: 98%

Lattice distortion near vacancies in diamond and silicon. I

Larkins

Stoneham

1971

J. Phys. C: Solid State Phys.

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Previous results (paper I), based on a dynamic relaxation procedure, coupled with a valence force potential function to represent the interaction between the atoms of the perfect crystal, have been used to calculate the distortion around point defects in a diamond-type crystal. The method has been applied to the isolated neutral vacancy in diamond and silicon for two alternative choices of rebonding forces for the vacancy electrons. In one case the electronic forces have been estimated from a detailed molecular orbital calculation, while in an alternative approach a generalized Morse-type potential relationship has been used. The formation energy of the neutral vacancy has also been calculated. For the vacancy in diamond values of 0.35 and 6.47 eV have been obtained using two alternative approximations to calculate the molecular orbital force terms, while with the Morse potential a value of-0.37 eV is obtained. The vacancy in silicon is estimated to have a formation energy of-38.8 eV using the molecular orbital parameters and-16.35 eV using the alternative method. The volume changes associated with the diamond-type system containing a vacancy are also calculated. The results suggest that one of the approximations used is not valid. Some of the possibilities are discussed.

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“…The entropy terms include both the configurational and the vibrational entropies. The energy of formation is determined by the atomic bonding at the defect site and the energy of migration is determined by the energy of the saddle point configuration 20 3.27 21 3.53 22 Ge 2.3 23 2.29 24 0.7 25 0.5 26 1.7-2.0 27 2.3-4.1 28 0.36-0.7 29 2.4 25 3.55 30 2.6 29 3.50 31 2.56 31 along the minimum energy transition path between stable atomic configurations.…”

Section: Introductionmentioning

confidence: 99%

Structure, energy, and electronic states of vacancies in Ge nanocrystals

2010

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The atomic structure, energy of formation, and electronic states of vacancies in H-passivated Ge nanocrystals are studied by density-functional theory methods. The competition between quantum self-purification and the free surface relaxations is investigated. The free surfaces of crystals smaller than 2 nm distort the Jahn-Teller relaxation and enhance the reconstruction bonds. This increases the energy splitting of the quantum states and reduces the energy of formation to as low as 1 eV per defect in the smallest nanocrystals. In crystals larger than 2 nm the observed symmetry of the Jahn-Teller distortion matches the symmetry expected for bulk Ge crystals. Near the nanocrystal's surface the vacancy is found to have an energy of formation no larger than 0.5-1.4 eV per defect, but a vacancy more than 0.7 nm inside the surface has an energy of formation that is the same as in bulk Ge. No evidence of the self-purification effect is observed; the dominant effect is the free surface relaxations, which allow for the enhanced reconstruction. From the evidence in this paper, it is predicted that for moderate sized Ge nanocrystals a vacancy inside the crystal will behave bulklike and not interact strongly with the surface, except when it is within 0.7 nm of the surface.

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Calculation of the Formation Energy of a Schottky Defect in Germanium

Cited by 17 publications

References 20 publications

Molecular dynamics simulation of intrinsic point defects in germanium

Molecular dynamics simulation of intrinsic point defects in germanium

Lattice distortion near vacancies in diamond and silicon. I

Structure, energy, and electronic states of vacancies in Ge nanocrystals

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